mkfun.tp {gss} | R Documentation |
Craft numerical functions to be used by mkterm.tp
to
assemble model terms.
mkrk.tp(dm,order,mesh,weight) mkphi.tp(dm,order,mesh,weight) mkrk.tp.p(dm,order) mkphi.tp.p(dm,order)
dm |
Dimension of the variable d. |
order |
Order of the differential operator m. |
mesh |
Normalizing mesh. |
weight |
Normalizing weights. |
Thin-plate splines are defined for 2m>d.
mkrk.tp.p
generates the pseudo kernel, and mkphi.tp.p
generates the (m+d-1)!/d!/(m-1)! lower order polynomials with
total order less than m.
mkphi.tp
generates normalized lower order polynomials
orthonormal w.r.t. a norm specified by mesh
and weight
as described in the reference, and mkrk.tp
conditions the
pseudo kernel to generate the reproducing kernel orthogonal to the
lower order polynomials w.r.t. the norm.
A list of two components.
fun |
Function definition. |
env |
Portable local constants derived from the arguments. |
mkrk.tp
creates a bivariate function
fun(x,y,env,outer=FALSE)
, where x
, y
are real
arguments and local constants can be passed in through env
.
mkphi.tp
creates a collection of univariate functions
fun(x,nu,env)
, where x
is the argument and nu
is the index.
Gu, C. and Wahba, G. (1993), Semiparametric analysis of variance with tensor product thin plate splines. Journal of the Royal Statistical Society Ser. B, 55, 353368.